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Advances in Pure and Applied Mathematics

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Lax's difference scheme for a system of two equations in the quarter plane

1School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India.

2Centre for Applicable Mathematics, Tata Institute of Fundamental Research, Sharadanagar, Chikkabommasandra, Bangalore 560065, India.

Citation Information: Advances in Pure and Applied Mathematics. Volume 2, Issue 2, Pages 167–181, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: 10.1515/apam.2010.033, August 2010

Publication History

Received:
2009-09-30
Published Online:
2010-08-03

Abstract

We extend a difference scheme introduced by Peter Lax for a scalar equation to a system of two conservation laws in the quarter plane {(x, t) : x > 0, t > 0} with initial conditions at t = 0 and conditions on the mass. We use Lax's transformation to linearize the problem and get an explicit formula for the solution. The limit generally belongs to the class of measures.

Keywords.: Difference scheme with boundary; solutions with given mass

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